Enhancing complex signal analysis via spectrally-driven nonlinear filtered cepstrum

Accurate time-frequency analysis of non-stationary and complex signals remains a significant challenge in various fields, such as acoustics, biomedical engineering, and signal processing. To address these limitations, this study proposes a novel Nonlinear Filtered Cepstrum (NFC) method, which leverages a dynamic nonlinear filter design to enhance the representation of intricate signal components. Specifically, the proposed method is driven by a spectral distribution that creates denser filters in the vicinity of those critical frequency peaks to achieve superior time-frequency resolution. More importantly, this method is adaptive and does not rely on the experience of an expert, which is a major advantage when dealing with unknown signals and massive data. Through detailed case studies involving simulation signal, chirp signal, ecological signal, and classical music signal, NFC demonstrates superior time-frequency resolution and robustness compared to conventional methods like Continuous Wavelet Transform, Constant-Q Transform, Mel Frequency Cepstrum and Wavelet Packet Energy Cepstrum. The results reveal that NFC excels in capturing key frequency components and minimizing irrelevant spectral information, especially under noisy conditions. While NFC incurs a higher computational burden, its enhanced adaptiveness and precision make it a promising tool for complex signal analysis.